%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU612^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:43 AM UTC 2026
% Result : Theorem 0.25s 0.26s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 4 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 238 ( 29 ~; 17 |; 4 &; 165 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 12 ^; 47 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrI: $o ).
thf(decl_26,type,
binunion: $i > $i > $i ).
thf(decl_27,type,
binunionIL: $o ).
thf(decl_28,type,
symdiff: $i > $i > $i ).
thf(decl_29,type,
esk1_0: $i ).
thf(decl_30,type,
esk2_0: $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(symdiffI1,conjecture,
( dsetconstrI
=> ( binunionIL
=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X5 )
=> ( in @ X3 @ ( symdiff @ X1 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fvD6ai9NMQ/E---3.1_756029.p',symdiffI1) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fvD6ai9NMQ/E---3.1_756029.p',dsetconstrI) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( binunion @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fvD6ai9NMQ/E---3.1_756029.p',binunionIL) ).
thf(symdiff,axiom,
( symdiff
= ( ^ [X1: $i,X5: $i] :
( dsetconstr @ ( binunion @ X1 @ X5 )
@ ^ [X3: $i] :
( ~ ( in @ X3 @ X1 )
| ~ ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fvD6ai9NMQ/E---3.1_756029.p',symdiff) ).
thf(c_0_4,negated_conjecture,
~ ( dsetconstrI
=> ( binunionIL
=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X5 )
=> ( in @ X3 @ ( symdiff @ X1 @ X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[symdiffI1]) ).
thf(c_0_5,plain,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o,X17: $i] :
( ( in @ X17 @ X15 )
=> ( ( X16 @ X17 )
=> ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) ) ) )
=> ( ! [X18: $i,X19: $i,X20: $i] :
( ( in @ X20 @ X18 )
=> ( in @ X20 @ ( binunion @ X18 @ X19 ) ) )
=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X5 )
=> ( in @ X3 @ ( symdiff @ X1 @ X5 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),binunionIL])])]) ).
thf(c_0_7,plain,
( symdiff
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( binunion @ Z0 @ Z1 )
@ ^ [Z2: $i] :
( ~ ( in @ Z2 @ Z0 )
| ~ ( in @ Z2 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[symdiff]) ).
thf(c_0_8,negated_conjecture,
! [X21: $i,X22: $i > $o,X23: $i,X24: $i,X25: $i,X26: $i] :
( ( ~ ( in @ X23 @ X21 )
| ~ ( X22 @ X23 )
| ( in @ X23 @ ( dsetconstr @ X21 @ X22 ) ) )
& ( ~ ( in @ X26 @ X24 )
| ( in @ X26 @ ( binunion @ X24 @ X25 ) ) )
& ( in @ esk3_0 @ esk1_0 )
& ~ ( in @ esk3_0 @ esk2_0 )
& ~ ( in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
thf(c_0_9,plain,
( symdiff
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( binunion @ Z0 @ Z1 )
@ ^ [Z2: $i] :
( ~ ( in @ Z2 @ Z0 )
| ~ ( in @ Z2 @ Z1 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X1: $i,X3: $i] :
( ( dsetconstr @ ( binunion @ X1 @ X3 )
@ ^ [Z0: $i] :
( ~ ( in @ Z0 @ X1 )
| ~ ( in @ Z0 @ X3 ) ) )
= ( symdiff @ X1 @ X3 ) ),
inference(arg_cong,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
| ~ ( ~ ( in @ X1 @ X3 )
| ~ ( in @ X1 @ X4 ) )
| ~ ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
| ( in @ X1 @ X4 )
| ~ ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
~ ( in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
| ( in @ X1 @ X4 )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU612^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:57:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.fvD6ai9NMQ/E---3.1_756029.p
% 0.25/0.26 % Version: 3.5.1-ho
% 0.25/0.26 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.25/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.26 % Starting full_lambda_3 with 300s (1) cores
% 0.25/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.25/0.26 % Starting sh4l with 300s (1) cores
% 0.25/0.26 % ho_unfolding_6 with pid 756060 completed with status 0
% 0.25/0.26 % Result found by ho_unfolding_6
% 0.25/0.26 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.25/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.26 % Starting full_lambda_3 with 300s (1) cores
% 0.25/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.25/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.26 % No SInE strategy applied
% 0.25/0.26 % Search class: HHUSF-FFSF22-DSFFMSBN
% 0.25/0.26 % partial match(1): HHUSF-FFSF22-SSFFMSBN
% 0.25/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.26 % SubtermCWHack with pid 756062 completed with status 0
% 0.25/0.26 % Result found by SubtermCWHack
% 0.25/0.26 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.25/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.26 % Starting full_lambda_3 with 300s (1) cores
% 0.25/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.25/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.26 % No SInE strategy applied
% 0.25/0.26 % Search class: HHUSF-FFSF22-DSFFMSBN
% 0.25/0.26 % partial match(1): HHUSF-FFSF22-SSFFMSBN
% 0.25/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.26 % Preprocessing time : 0.001 s
% 0.25/0.26
% 0.25/0.26 % Proof found!
% 0.25/0.26 % SZS status Theorem
% 0.25/0.26 % SZS output start CNFRefutation
% See solution above
% 0.25/0.26 % Parsed axioms : 10
% 0.25/0.26 % Removed by relevancy pruning/SinE : 0
% 0.25/0.26 % Initial clauses : 12
% 0.25/0.26 % Removed in clause preprocessing : 6
% 0.25/0.26 % Initial clauses in saturation : 6
% 0.25/0.26 % Processed clauses : 12
% 0.25/0.26 % ...of these trivial : 1
% 0.25/0.26 % ...subsumed : 0
% 0.25/0.26 % ...remaining for further processing : 11
% 0.25/0.26 % Other redundant clauses eliminated : 0
% 0.25/0.26 % Clauses deleted for lack of memory : 0
% 0.25/0.26 % Backward-subsumed : 0
% 0.25/0.26 % Backward-rewritten : 0
% 0.25/0.26 % Generated clauses : 8
% 0.25/0.26 % ...of the previous two non-redundant : 7
% 0.25/0.26 % ...aggressively subsumed : 0
% 0.25/0.26 % Contextual simplify-reflections : 0
% 0.25/0.26 % Paramodulations : 3
% 0.25/0.26 % Factorizations : 0
% 0.25/0.26 % NegExts : 0
% 0.25/0.26 % Equation resolutions : 0
% 0.25/0.26 % Disequality decompositions : 0
% 0.25/0.26 % Total rewrite steps : 2
% 0.25/0.26 % ...of those cached : 0
% 0.25/0.26 % Propositional unsat checks : 0
% 0.25/0.26 % Propositional check models : 0
% 0.25/0.26 % Propositional check unsatisfiable : 0
% 0.25/0.26 % Propositional clauses : 0
% 0.25/0.26 % Propositional clauses after purity: 0
% 0.25/0.26 % Propositional unsat core size : 0
% 0.25/0.26 % Propositional preprocessing time : 0.000
% 0.25/0.26 % Propositional encoding time : 0.000
% 0.25/0.26 % Propositional solver time : 0.000
% 0.25/0.26 % Success case prop preproc time : 0.000
% 0.25/0.26 % Success case prop encoding time : 0.000
% 0.25/0.26 % Success case prop solver time : 0.000
% 0.25/0.26 % Current number of processed clauses : 10
% 0.25/0.26 % Positive orientable unit clauses : 4
% 0.25/0.26 % Positive unorientable unit clauses: 0
% 0.25/0.26 % Negative unit clauses : 2
% 0.25/0.26 % Non-unit-clauses : 4
% 0.25/0.26 % Current number of unprocessed clauses: 1
% 0.25/0.26 % ...number of literals in the above : 3
% 0.25/0.26 % Current number of archived formulas : 0
% 0.25/0.26 % Current number of archived clauses : 1
% 0.25/0.26 % Clause-clause subsumption calls (NU) : 4
% 0.25/0.26 % Rec. Clause-clause subsumption calls : 3
% 0.25/0.26 % Non-unit clause-clause subsumptions : 0
% 0.25/0.26 % Unit Clause-clause subsumption calls : 0
% 0.25/0.26 % Rewrite failures with RHS unbound : 0
% 0.25/0.26 % BW rewrite match attempts : 1
% 0.25/0.26 % BW rewrite match successes : 0
% 0.25/0.26 % Condensation attempts : 0
% 0.25/0.26 % Condensation successes : 0
% 0.25/0.26 % Termbank termtop insertions : 1117
% 0.25/0.26 % Search garbage collected termcells : 236
% 0.25/0.26
% 0.25/0.26 % -------------------------------------------------
% 0.25/0.26 % User time : 0.005 s
% 0.25/0.26 % System time : 0.001 s
% 0.25/0.26 % Total time : 0.006 s
% 0.25/0.26 % Maximum resident set size: 3636 pages
% 0.25/0.26
% 0.25/0.26 % -------------------------------------------------
% 0.25/0.26 % User time : 0.007 s
% 0.25/0.26 % System time : 0.006 s
% 0.25/0.26 % Total time : 0.013 s
% 0.25/0.26 % Maximum resident set size: 4864 pages
% 0.25/0.26 % E exiting
%------------------------------------------------------------------------------